2017
8
2
0
137
A novel topological descriptor based on the expanded wiener index: Applications to QSPR/QSAR studies
2
2
In this paper, a novel topological index, named Mindex, is introduced based on expanded form of the Wiener matrix. For constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. The usefulness of the Mindex is demonstrated by several QSPR/QSAR models for different physicochemical properties and biological activities of a large number of diversified compounds. Moreover, the applicability of the proposed index has been checked among isomeric compounds. In each case the stability of the obtained model is confirmed by the cross validation test. The results of present study indicate that the Mindex provides a promising route for developing highly correlated QSPR/QSAR models. On the other hand, the Mindex is easy to generate and the developed QSPR/QSAR models based on this index are linearly correlated. This is an interesting feature of the Mindex when compared with quantum chemical descriptors which require vast computational cost and exhibit limitations for large sized molecules.
1

107
135


A.
Mohajeri
Shiraz University
Shiraz University
I R Iran
mohajeriaf@gmail.com


P.
Manshour
Persian Gulf University
Persian Gulf University
I R Iran


M.
Mousaee
Shiraz University
Shiraz University
I R Iran
mahboub.mousaee@gmail.com
Topological index
Graph theory
Expanded Wiener index
QSPR
QSAR
A new twostep Obrechkoff method with vanished phaselag and some of its derivatives for the numerical solution of radial Schrodinger equation and related IVPs with oscillating solutions
2
2
A new twostep implicit linear Obrechkoff twelfth algebraic order method with vanished phaselag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the onedimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phaselag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.
1

137
159


A.
Shokri
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic
I R Iran
shokri2090@gmail.com


M.
Tahmourasi
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic
I R Iran
mortazatahmoras@gmail.com
Schrodinger equation
Phaselag
Ordinary differential equations
Symmetric multistep methods
Optimal control of switched systems by a modified pseudo spectral method
2
2
In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many realworld processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching times appear as unknown parameters. Using the LegendreGaussLobatto quadrature and the corresponding differentiation matrix, the alternative problem is discretized to a nonlinear programming problem. At last, we examine three examples in order to illustrate the efficiency of the proposed method.
1

161
173


H.
Tabrizidooz
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty
I R Iran
htabrizidooz@kashanu.ac.ir


M.
Pourbabaee
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty
I R Iran
m.pourbabaee@kashanu.ac.ir


M.
Hedayati
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty
I R Iran
mehrhedayati@yahoo.com
Optimal Control
switched systems
Legendre pseudospectral method
Computing Szeged index of graphs on triples
2
2
ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define three types of intersection graphs with vertex set V. These graphs are denoted by and we will find their Szeged indices.
1

175
180


M.
Darafsheh
School of Mathematics, College of Science, University of Tehran
School of Mathematics, College of Science,
I R Iran
darafsheh@ut.ac.ir


R.
Modabernia
Department of Mathematics, Shahid Chamran University of Ahvaz
Department of Mathematics, Shahid Chamran
I R Iran
r.modabber@yahoo.com


M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz
Department of Mathematics, Shahid Chamran
I R Iran
namdari@ipm.ir
Szeged index
Intersection graph
Automorphism of graph
NordhausGaddum type results for the Harary index of graphs
2
2
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ of the vertices of $S$ is the minimum size of a connected subgraph whose vertex set contains $S$. Recently, Furtula, Gutman, and Katani'{c} introduced the concept of Steiner Harary index and gave its chemical applications. The emph{$k$center Steiner Harary index} $SH_k(G)$ of $G$ is defined by $SH_k(G)=sum_{Ssubseteq V(G),S=k}frac{1}{d_G(S)}$. In this paper, we get the sharp upper and lower bounds for $SH_k(G)+SH_k(overline{G})$ and $SH_k(G)cdot SH_k(overline{G})$, valid for any connected graph $G$ whose complement $overline {G}$ is also connected.
1

181
198


Z.
Wang
Beijing Normal Unviersity
Beijing Normal Unviersity
P. R. China
wangzhao580@yahoo.com


Y.
Mao
Qinghai Normal Unviersity
Qinghai Normal Unviersity
P. R. China
maoyaping@ymail.com


X.
Wang
Qinghai Normal University
Qinghai Normal University
P. R. China
wangxiaia@163.com


C.
Wang
Qinghai Normal Unviersity
Qinghai Normal Unviersity
P. R. China
wangchunxiaia@163.com
Distance
Steiner distance
Harary index
Kcenter Steiner Harary index
Determination of critical properties of Alkanes derivatives using multiple linear regression
2
2
This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as HyperWiener, Platt, MinZL is the most appropriate one.
1

199
220


E.
Mohammadinasab
Islamic Azad University of Arak Branch
Islamic Azad University of Arak Branch
I R Iran
esmohammadinasab@gmail.com
Alkanes
MLR
Critical Properties
QSPR
Some relations between Kekule structure and MorganVoyce polynomials
2
2
In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) MorganVoyce polynomial equal to the number of kmatchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zigzag nonbranched catacondensed benzenid chains and MorganVoyce polynomials and between regularly zigzag nonbranched catacondensed benzenid chains and their corresponding caterpillar trees.
1

221
229


I.
Gultekin
Ataturk University
Ataturk University
Turkey
igultekin@atauni.edu.tr


B.
Sahin
bayburt university
bayburt university
Turkey
bsahin@bayburt.edu.tr
Kekule structure
Hosoya Index
MorganVoyce polynomial
Caterpillar Tree